Adding and subtracting within 20
Students solve story problems by adding and taking away. They learn to count on from a number instead of starting at one, and to see how addition and subtraction undo each other.
This is the year math stretches past counting into thinking in tens and ones. Students add and subtract within 20, learn that a number like 47 is four tens and seven ones, and start comparing two-digit numbers. They also measure objects with a ruler, read a clock to the hour and half hour, and name shapes by what makes them that shape. By spring, students can solve a word problem like 8 plus 6 in their head and split a circle into halves and fourths.
Students solve story problems by adding and taking away. They learn to count on from a number instead of starting at one, and to see how addition and subtraction undo each other.
Students count all the way to 120 and start to see numbers like 34 as three tens and four ones. They compare two numbers and tell which is bigger using the signs greater than, less than, and equal to.
Students add a small number to a larger one, like 47 plus 6, and add tens like 30 plus 50. They use drawings and grouping by ten to keep track, and learn to find ten more or ten less in their head.
Students line up objects to compare how long they are and measure with paper clips or cubes. They read clocks at the hour and half hour, and sort information into simple charts to answer questions.
Students build and draw shapes, noticing what makes a triangle a triangle and not just any closed figure. They cut circles and rectangles into halves and fourths, and see that more pieces means smaller pieces.
Students read a math problem all the way through, figure out what it's asking, and keep trying even when the first approach doesn't work.
Students take a real problem (like sharing 8 crayons between 2 friends) and turn it into numbers to solve it, then check whether the answer makes sense in the original situation.
Students explain why their math answer makes sense and listen to a classmate's explanation to decide if it holds up. They learn that "because I said so" isn't enough.
Students use drawings, number sentences, or simple diagrams to show a real-world problem, like sharing snacks or counting coins. The picture or equation is the model.
Students learn to pick the right tool for the job, whether that means grabbing a ruler, counting blocks, or drawing a picture. Knowing when each tool helps is part of the math itself.
Students say exactly what they mean when explaining math. They use the right words, label their answers with units like inches or dollars, and check that their numbers are accurate.
Students learn to spot patterns in math, like noticing that 3 + 5 and 5 + 3 give the same answer, then use those patterns as shortcuts to solve new problems.
Students notice when the same steps keep working the same way, like adding zero always leaves a number unchanged. They use that pattern as a shortcut instead of starting from scratch each time.
| Standard | Definition | Code |
|---|---|---|
| Make sense of problems and persevere in solving them | Students read a math problem all the way through, figure out what it's asking, and keep trying even when the first approach doesn't work. | CCSS.Math.Practice.MP1 |
| Reason abstractly and quantitatively | Students take a real problem (like sharing 8 crayons between 2 friends) and turn it into numbers to solve it, then check whether the answer makes sense in the original situation. | CCSS.Math.Practice.MP2 |
| Construct viable arguments and critique the reasoning of others | Students explain why their math answer makes sense and listen to a classmate's explanation to decide if it holds up. They learn that "because I said so" isn't enough. | CCSS.Math.Practice.MP3 |
| Model with mathematics | Students use drawings, number sentences, or simple diagrams to show a real-world problem, like sharing snacks or counting coins. The picture or equation is the model. | CCSS.Math.Practice.MP4 |
| Use appropriate tools strategically | Students learn to pick the right tool for the job, whether that means grabbing a ruler, counting blocks, or drawing a picture. Knowing when each tool helps is part of the math itself. | CCSS.Math.Practice.MP5 |
| Attend to precision | Students say exactly what they mean when explaining math. They use the right words, label their answers with units like inches or dollars, and check that their numbers are accurate. | CCSS.Math.Practice.MP6 |
| Look for and make use of structure | Students learn to spot patterns in math, like noticing that 3 + 5 and 5 + 3 give the same answer, then use those patterns as shortcuts to solve new problems. | CCSS.Math.Practice.MP7 |
| Look for and express regularity in repeated reasoning | Students notice when the same steps keep working the same way, like adding zero always leaves a number unchanged. They use that pattern as a shortcut instead of starting from scratch each time. | CCSS.Math.Practice.MP8 |
Students use pictures, objects, and simple equations to figure out addition and subtraction problems. This is the foundation for all the math story problems they will solve in first grade.
Students read short word problems and figure out whether to add or subtract numbers up to 20. The unknown number can appear anywhere in the problem, so students practice finding what's missing, what's left, or how many there are altogether.
Students add three small numbers together to solve a simple story problem, like figuring out how many apples there are across three baskets. The total is always 20 or less.
Addition and subtraction are two sides of the same problem. Students learn that if 3 + 5 = 8, then 8 - 5 = 3, and use that connection to solve equations faster.
Switching the order of two numbers being added still gives the same total. Students use this idea as a shortcut, so if they know 3 + 5, they already know 5 + 3.
Subtracting is the same as asking "what number do I add to get there?" Students learn to solve 10 minus 7 by asking what goes with 7 to make 10.
Students practice adding and subtracting with numbers up to 20. The focus is on building enough fluency that students can solve these problems quickly and accurately on their own.
Counting up or back on a number line is the same move as adding or subtracting. Students practice starting at a number and counting forward to add, or counting backward to subtract.
Students add and subtract numbers up to 20, and do it quickly and reliably up to 10. They use shortcuts like counting forward from a number or breaking numbers apart to make a 10 first.
Students practice writing and solving addition and subtraction equations, learning that the equals sign means both sides of the number sentence have the same value.
The equal sign means "the same amount on both sides." Students look at addition and subtraction equations and decide whether both sides match, judging if a statement like 6 = 3 + 3 is true or false.
Students find the missing number in an addition or subtraction problem, like figuring out what goes in the blank in 5 + __ = 9. They work with all three numbers in the equation to solve it.
| Standard | Definition | Code |
|---|---|---|
| Represent and solve problems involving addition and subtraction | Students use pictures, objects, and simple equations to figure out addition and subtraction problems. This is the foundation for all the math story problems they will solve in first grade. | CCSS.Math.Content.1.OA.A |
| Use addition and subtraction within 20 to solve word problems involving… | Students read short word problems and figure out whether to add or subtract numbers up to 20. The unknown number can appear anywhere in the problem, so students practice finding what's missing, what's left, or how many there are altogether. | CCSS.Math.Content.1.OA.A.1 |
| Solve word problems that call for addition of three whole numbers whose sum is… | Students add three small numbers together to solve a simple story problem, like figuring out how many apples there are across three baskets. The total is always 20 or less. | CCSS.Math.Content.1.OA.A.2 |
| Understand and apply properties of operations and the relationship between… | Addition and subtraction are two sides of the same problem. Students learn that if 3 + 5 = 8, then 8 - 5 = 3, and use that connection to solve equations faster. | CCSS.Math.Content.1.OA.B |
| Apply properties of operations as strategies to add and subtract | Switching the order of two numbers being added still gives the same total. Students use this idea as a shortcut, so if they know 3 + 5, they already know 5 + 3. | CCSS.Math.Content.1.OA.B.3 |
| Understand subtraction as an unknown-addend problem | Subtracting is the same as asking "what number do I add to get there?" Students learn to solve 10 minus 7 by asking what goes with 7 to make 10. | CCSS.Math.Content.1.OA.B.4 |
| Add and subtract within 20 | Students practice adding and subtracting with numbers up to 20. The focus is on building enough fluency that students can solve these problems quickly and accurately on their own. | CCSS.Math.Content.1.OA.C |
| Relate counting to addition and subtraction | Counting up or back on a number line is the same move as adding or subtracting. Students practice starting at a number and counting forward to add, or counting backward to subtract. | CCSS.Math.Content.1.OA.C.5 |
| Add and subtract within 20, demonstrating fluency for addition and subtraction… | Students add and subtract numbers up to 20, and do it quickly and reliably up to 10. They use shortcuts like counting forward from a number or breaking numbers apart to make a 10 first. | CCSS.Math.Content.1.OA.C.6 |
| Work with addition and subtraction equations | Students practice writing and solving addition and subtraction equations, learning that the equals sign means both sides of the number sentence have the same value. | CCSS.Math.Content.1.OA.D |
| Understand the meaning of the equal sign | The equal sign means "the same amount on both sides." Students look at addition and subtraction equations and decide whether both sides match, judging if a statement like 6 = 3 + 3 is true or false. | CCSS.Math.Content.1.OA.D.7 |
| Determine the unknown whole number in an addition or subtraction equation… | Students find the missing number in an addition or subtraction problem, like figuring out what goes in the blank in 5 + __ = 9. They work with all three numbers in the equation to solve it. | CCSS.Math.Content.1.OA.D.8 |
Students learn to count past 100, reading and writing numbers in order. They practice counting forward and backward so the sequence of numbers feels automatic.
Students count, read, and write numbers up to 120, starting from any number, not just 1. They also look at a group of objects and write the number that shows how many.
Students learn that the position of a digit changes its value. A 2 in the tens place means twenty, not two.
A two-digit number like 47 means 4 tens and 7 ones, not just a string of digits. Students learn to break apart numbers this way so place value makes sense before they start adding and subtracting larger numbers.
Students learn that 10 individual ones can be grouped together and treated as a single unit called a "ten." This is the building block for understanding how two-digit numbers work.
Numbers like 13 or 17 are built from one group of ten plus some leftover ones. Students practice breaking apart these numbers to see the ten hiding inside them.
The round numbers on the decade (10, 20, 30, up to 90) are just a count of tens with nothing left over. 20 means two tens, 50 means five tens, and so on.
Students look at two numbers up to 99 and decide which is bigger, smaller, or equal. They record the answer using the symbols >, <, or =.
Students use what they know about tens and ones to add and subtract numbers. They learn reliable methods for combining and breaking apart numbers, not just memorizing steps.
Students add numbers up to 100 by grouping tens and ones separately. For example, adding 36 + 7 means handling the ones first, then figuring out if ten of them need to be bundled together.
Students pick a two-digit number and figure out in their head what it looks like with ten more or ten fewer, without counting up or back. Then they explain how they knew.
Students subtract tens from tens, like 70 minus 40, using blocks, drawings, or number patterns. They explain how they got the answer and connect it to what they know about adding.
| Standard | Definition | Code |
|---|---|---|
| Extend the counting sequence | Students learn to count past 100, reading and writing numbers in order. They practice counting forward and backward so the sequence of numbers feels automatic. | CCSS.Math.Content.1.NBT.A |
| Count to 120, starting at any number less than 120 | Students count, read, and write numbers up to 120, starting from any number, not just 1. They also look at a group of objects and write the number that shows how many. | CCSS.Math.Content.1.NBT.A.1 |
| Understand place value | Students learn that the position of a digit changes its value. A 2 in the tens place means twenty, not two. | CCSS.Math.Content.1.NBT.B |
| Understand that the two digits of a two-digit number represent amounts of tens… | A two-digit number like 47 means 4 tens and 7 ones, not just a string of digits. Students learn to break apart numbers this way so place value makes sense before they start adding and subtracting larger numbers. | CCSS.Math.Content.1.NBT.B.2 |
| 10 can be thought of as a bundle of ten ones — called a "ten." | Students learn that 10 individual ones can be grouped together and treated as a single unit called a "ten." This is the building block for understanding how two-digit numbers work. | CCSS.Math.Content.1.NBT.B.2a |
| The numbers from 11 to 19 are composed of a ten and one, two, three, four… | Numbers like 13 or 17 are built from one group of ten plus some leftover ones. Students practice breaking apart these numbers to see the ten hiding inside them. | CCSS.Math.Content.1.NBT.B.2b |
| The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four… | The round numbers on the decade (10, 20, 30, up to 90) are just a count of tens with nothing left over. 20 means two tens, 50 means five tens, and so on. | CCSS.Math.Content.1.NBT.B.2c |
| Compare two two-digit numbers based on meanings of the tens and ones digits… | Students look at two numbers up to 99 and decide which is bigger, smaller, or equal. They record the answer using the symbols >, <, or =. | CCSS.Math.Content.1.NBT.B.3 |
| Use place value understanding and properties of operations to add and subtract | Students use what they know about tens and ones to add and subtract numbers. They learn reliable methods for combining and breaking apart numbers, not just memorizing steps. | CCSS.Math.Content.1.NBT.C |
| Add within 100, including adding a two-digit number and a one-digit number | Students add numbers up to 100 by grouping tens and ones separately. For example, adding 36 + 7 means handling the ones first, then figuring out if ten of them need to be bundled together. | CCSS.Math.Content.1.NBT.C.4 |
| Given a two-digit number, mentally find 10 more or 10 less than the number… | Students pick a two-digit number and figure out in their head what it looks like with ten more or ten fewer, without counting up or back. Then they explain how they knew. | CCSS.Math.Content.1.NBT.C.5 |
| Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range… | Students subtract tens from tens, like 70 minus 40, using blocks, drawings, or number patterns. They explain how they got the answer and connect it to what they know about adding. | CCSS.Math.Content.1.NBT.C.6 |
Students measure how long something is by lining up small objects end to end and counting them. They also compare lengths by using a third object as a go-between when two things can't be placed side by side.
Line up three objects from shortest to longest. Students also figure out which of two objects is longer by comparing each one to a third object, like a piece of string.
Students measure how long something is by lining up small objects end to end, like placing paper clips in a row across a pencil. The count of objects, with no gaps or spaces between them, is the length.
Students read a clock and write down the time it shows, starting with hours and then half-hours.
Students read a clock and write down the time, working with whole hours (like 3:00) and half-hours (like 3:30). They practice with both the round analog clock face and digital displays.
Students collect simple information, like favorite colors or how many teeth they've lost, then organize it into a picture or tally chart so the class can read and compare the results.
Students sort objects or answers into up to three groups, then count each group and compare them. They practice reading simple charts and answering questions like "How many more chose cats than dogs?"
| Standard | Definition | Code |
|---|---|---|
| Measure lengths indirectly and by iterating length units | Students measure how long something is by lining up small objects end to end and counting them. They also compare lengths by using a third object as a go-between when two things can't be placed side by side. | CCSS.Math.Content.1.MD.A |
| Order three objects by length | Line up three objects from shortest to longest. Students also figure out which of two objects is longer by comparing each one to a third object, like a piece of string. | CCSS.Math.Content.1.MD.A.1 |
| Express the length of an object as a whole number of length units, by laying… | Students measure how long something is by lining up small objects end to end, like placing paper clips in a row across a pencil. The count of objects, with no gaps or spaces between them, is the length. | CCSS.Math.Content.1.MD.A.2 |
| Tell and write time | Students read a clock and write down the time it shows, starting with hours and then half-hours. | CCSS.Math.Content.1.MD.B |
| Tell and write time in hours and half-hours using analog and digital clocks | Students read a clock and write down the time, working with whole hours (like 3:00) and half-hours (like 3:30). They practice with both the round analog clock face and digital displays. | CCSS.Math.Content.1.MD.B.3 |
| Represent and interpret data | Students collect simple information, like favorite colors or how many teeth they've lost, then organize it into a picture or tally chart so the class can read and compare the results. | CCSS.Math.Content.1.MD.C |
| Organize, represent, and interpret data with up to three categories | Students sort objects or answers into up to three groups, then count each group and compare them. They practice reading simple charts and answering questions like "How many more chose cats than dogs?" | CCSS.Math.Content.1.MD.C.4 |
Students sort, compare, and build flat and solid shapes by describing what makes them alike or different, such as the number of sides or whether a face is flat.
Students learn which features actually make a shape what it is. A triangle is always three-sided, but its color or size do not matter. Students sort, build, and draw shapes based on the rules that count.
Students put simple shapes together to build a new, bigger shape, then use that new shape as a building block to make something even bigger.
Students cut circles and rectangles into two or four equal pieces and name each piece a half, a fourth, or a quarter. Splitting a shape into more equal pieces makes each piece smaller.
| Standard | Definition | Code |
|---|---|---|
| Reason with shapes and their attributes | Students sort, compare, and build flat and solid shapes by describing what makes them alike or different, such as the number of sides or whether a face is flat. | CCSS.Math.Content.1.G.A |
| Distinguish between defining attributes | Students learn which features actually make a shape what it is. A triangle is always three-sided, but its color or size do not matter. Students sort, build, and draw shapes based on the rules that count. | CCSS.Math.Content.1.G.A.1 |
| Compose two-dimensional shapes | Students put simple shapes together to build a new, bigger shape, then use that new shape as a building block to make something even bigger. | CCSS.Math.Content.1.G.A.2 |
| Partition circles and rectangles into two and four equal shares, describe the… | Students cut circles and rectangles into two or four equal pieces and name each piece a half, a fourth, or a quarter. Splitting a shape into more equal pieces makes each piece smaller. | CCSS.Math.Content.1.G.A.3 |
Students add and subtract within 20, count to 120, and start working with tens and ones. They also tell time to the hour and half-hour, measure with small units like paper clips, and name shapes by what makes them that shape. Word problems show up almost every day.
Roll two dice and race to add the numbers. Count steps to the mailbox and back. Ask how many minutes until a show starts at 7:30. Hand over coins and ask for the total. Small daily moments beat long worksheets at this age.
Fingers are a normal first-grade tool. Over the year, students move from counting every finger to counting on from the bigger number, then to knowing pairs that make ten. The goal by spring is quick recall for sums within 10, with strategies for the rest.
Start with counting on and small sums, then build the make-ten strategy and doubles. Move into subtraction as a missing addend before pushing standard facts. Save two-digit addition and ten more or ten less for the back half of the year, once place value is steady.
Students fluently add and subtract within 10, solve word problems within 20 with a strategy they can explain, and read and write numbers to 120. They can compare two-digit numbers, tell time to the half-hour, and split a shape into halves and fourths.
The meaning of the equal sign, subtraction as a missing addend, and place value for the teen numbers. Many students read 14 as a single chunk rather than a ten and four ones. Plan extra time on these before moving into two-digit addition.
Read the problem twice and ask what is happening before asking for an answer. Let students draw circles, tallies, or a quick sketch. Then ask them to say the story back in their own words. Getting the situation right matters more than picking the right operation on the first try.
Look for quick recall of sums within 10, comfort solving word problems within 20, and clear use of tens and ones up to 100. Students should tell time to the half-hour, measure a pencil with same-size units, and name halves and fourths of a shape.
Plan short, regular units rather than one long stretch. A week on length, a week on time, and a week on shapes spread across the year keeps these skills fresh. Tuck quick shape and measurement warm-ups into number units so students keep practicing.